Question

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass $= 5.98 \times 10^{24} \, kg$) have to be compressed to be a black hole?

• A. $10^{-9} \, m$
• B. $10^{-6} \, m$
• C. $10^{-2} \, m$
• D. $100\, m$

Answer 1

The Correct Option is C

Light cannot escape from a black hole,
$v_{esc} = c$
$\sqrt \frac {2GM}{R} = c$ or $R = \frac {2GM}{c^2}$
$R = \frac {2\, \times \,6.67 \times 10^{-11}\,N \,m^2\, kg^{-2}\, \times \,5.98\, \times \,10^{24}\,kg}{(3 \,\times \,10^8 \,ms^{-1})^2}$
$ = 8.86 \times 10^{-3} \,m \approx 10 ^{-2}\, m $